A student is playing a game that begins with three coins, each with heads showing. At each turn, the student turns over exactly two of the three coins.
a. After the first turn, how many heads are showing? b. Suppose an odd number of heads are showing. Explain why taking one
turn cannot produce an even number of heads.
c. Using the result from part (b), explain why the student will never get exactly 2 heads showing.
Cover Me
Two FBI agents arrive at a dangerous junkyard, at position K. As a shootout ensues, they receive a local map on their cell phones. The circles represent regions of safety. If one agent stays on a colored circle, and covers for their partner, then the partner may safely run along paths of that color. In order to apprehend the suspect, both agents must arrive safely at circle I. For example, KK (start with two agents on K) - KP (agent on yellow K covers for partn
er's run on yellow path) - AP (agent on yellow P covers for partner's run on yellow path) - AF (agent on red A covers for partner's run on red path) - AA (agent on red A covers for partner's run on red path) - AB. But this seems to be a dead end. Can you guide the two agents to I, safely? Write the steps out below the picture.
